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Semiclassical Quantization in Many Dimensions


Williams, Roy David (1983) Semiclassical Quantization in Many Dimensions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ezwt-k047.


We examine the semiclassical limit of the quantum energy spectrum in many dimensions: by means of a WKB-like ansatz leading to Einstein-Brillouin-Keller (EBK) quantization, by means of a path integral, hence associating a bound state with a particular classical periodic trajectory, and by the Birkhoff-Gustavson (BG) transformation to action-angle variables. We extend the EBK method to many-fermion systems using coherent states; and apply both EBK using surfaces of section, and the BG transformation to an SU(3) schematic nuclear shell model. We describe a new algorithm for finding periodic trajectories of a Lagrangian system with polynomial potential. It is applied to the Henon-Heiles system with good results, and these trajectories are used to quantize the system. The EBK and BG methods have some success, while periodic trajectory quantization fails. We discuss possible reasons for this failure and future approaches to these problems.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Physics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Koonin, Steven E.
Thesis Committee:
  • Koonin, Steven E. (chair)
  • Barnes, Charles A.
  • Frautschi, Steven C.
  • Simon, Barry M.
Defense Date:25 April 1983
Record Number:CaltechTHESIS:10312019-103914805
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11876
Deposited By: Mel Ray
Deposited On:31 Oct 2019 17:54
Last Modified:16 Apr 2021 23:17

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